How many terms of AP: 24,21,18........ must be taken so that their sum is 78
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Given A.P is
24,21,18,....
a = 24
D = 21- 24 =-3
Sn = 78
n/2{2a + (n-1)d} =78
n/2{2(24) +(n-1)(-3)} = 78
n/2{48 -3n + 3} = 78
48n/2 - 3n^2/2 + 3/2 = 78
- 1/2 { 3n^2 -48n -3 } = 78
3n^2 - 48n - 3= 78(-2)
3n^2 - 48n = -156
3n^2 - 48n + 156 -3= 0
3n^2 - 48n + 153 = 0
3(n^2 - 16n + 51)= 0
n^2 - 16n + 51 = 0
using squaring method
D = (b)^2 - 4ac
= (16)^2 - 4(1)(51)
= 258 - 204
= 54
√ D = √54
n = -(b)- √D/2(a)
n = 16 +- √54/2
n = 16 +3√6/2
or
n = 16 - 3√6/2
Hope it helps you
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